TSTP Solution File: SWC020+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC020+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 31 12:38:54 EDT 2023

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   87 (  11 unt;   0 def)
%            Number of atoms       :  253 (  49 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  264 (  98   ~;  98   |;  41   &)
%                                         (  15 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   19 (  17 usr;  14 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   40 (;  30   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,axiom,
    ! [U] :
      ( ssList(U)
     => frontsegP(U,U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,axiom,
    ! [U] :
      ( ssList(U)
     => frontsegP(U,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f46,axiom,
    ! [U] :
      ( ssList(U)
     => ( frontsegP(nil,U)
      <=> nil = U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ? [Y] :
                        ( ssList(Y)
                        & neq(Y,nil)
                        & frontsegP(V,Y)
                        & frontsegP(U,Y) )
                    | ( nil = V
                      & nil = U )
                    | ( ( nil != X
                        | nil != W )
                      & ( ~ neq(W,nil)
                        | ~ frontsegP(X,W) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f97,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( V != X
                      | U != W
                      | ? [Y] :
                          ( ssList(Y)
                          & neq(Y,nil)
                          & frontsegP(V,Y)
                          & frontsegP(U,Y) )
                      | ( nil = V
                        & nil = U )
                      | ( ( nil != X
                          | nil != W )
                        & ( ~ neq(W,nil)
                          | ~ frontsegP(X,W) ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f223,plain,
    ssList(nil),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f285,plain,
    ! [U] :
      ( ~ ssList(U)
      | frontsegP(U,U) ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f286,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f285]) ).

fof(f294,plain,
    ! [U] :
      ( ~ ssList(U)
      | frontsegP(U,nil) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f295,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,nil) ),
    inference(cnf_transformation,[status(esa)],[f294]) ).

fof(f296,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( frontsegP(nil,U)
      <=> nil = U ) ),
    inference(pre_NNF_transformation,[status(esa)],[f46]) ).

fof(f297,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ frontsegP(nil,U)
          | nil = U )
        & ( frontsegP(nil,U)
          | nil != U ) ) ),
    inference(NNF_transformation,[status(esa)],[f296]) ).

fof(f298,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ frontsegP(nil,X0)
      | nil = X0 ),
    inference(cnf_transformation,[status(esa)],[f297]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ! [Y] :
                      ( ~ ssList(Y)
                      | ~ neq(Y,nil)
                      | ~ frontsegP(V,Y)
                      | ~ frontsegP(U,Y) )
                  & ( nil != V
                    | nil != U )
                  & ( ( nil = X
                      & nil = W )
                    | ( neq(W,nil)
                      & frontsegP(X,W) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ! [W,X] :
      ( pd0_0(X,W)
     => ( nil = X
        & nil = W ) ),
    introduced(predicate_definition,[f415]) ).

fof(f417,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ! [Y] :
                      ( ~ ssList(Y)
                      | ~ neq(Y,nil)
                      | ~ frontsegP(V,Y)
                      | ~ frontsegP(U,Y) )
                  & ( nil != V
                    | nil != U )
                  & ( pd0_0(X,W)
                    | ( neq(W,nil)
                      & frontsegP(X,W) ) ) ) ) ) ),
    inference(formula_renaming,[status(thm)],[f415,f416]) ).

fof(f418,plain,
    ( ssList(sk0_47)
    & ssList(sk0_48)
    & ssList(sk0_49)
    & ssList(sk0_50)
    & sk0_48 = sk0_50
    & sk0_47 = sk0_49
    & ! [Y] :
        ( ~ ssList(Y)
        | ~ neq(Y,nil)
        | ~ frontsegP(sk0_48,Y)
        | ~ frontsegP(sk0_47,Y) )
    & ( nil != sk0_48
      | nil != sk0_47 )
    & ( pd0_0(sk0_50,sk0_49)
      | ( neq(sk0_49,nil)
        & frontsegP(sk0_50,sk0_49) ) ) ),
    inference(skolemization,[status(esa)],[f417]) ).

fof(f419,plain,
    ssList(sk0_47),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f420,plain,
    ssList(sk0_48),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f423,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f424,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f425,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ neq(X0,nil)
      | ~ frontsegP(sk0_48,X0)
      | ~ frontsegP(sk0_47,X0) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f426,plain,
    ( nil != sk0_48
    | nil != sk0_47 ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f427,plain,
    ( pd0_0(sk0_50,sk0_49)
    | neq(sk0_49,nil) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f428,plain,
    ( pd0_0(sk0_50,sk0_49)
    | frontsegP(sk0_50,sk0_49) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f429,plain,
    ! [W,X] :
      ( ~ pd0_0(X,W)
      | ( nil = X
        & nil = W ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

fof(f430,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | nil = X0 ),
    inference(cnf_transformation,[status(esa)],[f429]) ).

fof(f431,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | nil = X1 ),
    inference(cnf_transformation,[status(esa)],[f429]) ).

fof(f432,plain,
    ( spl0_0
  <=> nil = sk0_48 ),
    introduced(split_symbol_definition) ).

fof(f434,plain,
    ( nil != sk0_48
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f432]) ).

fof(f435,plain,
    ( spl0_1
  <=> nil = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f437,plain,
    ( nil != sk0_47
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f435]) ).

fof(f438,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f426,f432,f435]) ).

fof(f439,plain,
    ( spl0_2
  <=> pd0_0(sk0_50,sk0_49) ),
    introduced(split_symbol_definition) ).

fof(f440,plain,
    ( pd0_0(sk0_50,sk0_49)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f439]) ).

fof(f442,plain,
    ( spl0_3
  <=> neq(sk0_49,nil) ),
    introduced(split_symbol_definition) ).

fof(f443,plain,
    ( neq(sk0_49,nil)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f442]) ).

fof(f445,plain,
    ( spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f427,f439,f442]) ).

fof(f446,plain,
    ( spl0_4
  <=> frontsegP(sk0_50,sk0_49) ),
    introduced(split_symbol_definition) ).

fof(f447,plain,
    ( frontsegP(sk0_50,sk0_49)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f446]) ).

fof(f449,plain,
    ( spl0_2
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f428,f439,f446]) ).

fof(f482,plain,
    ( spl0_5
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f484,plain,
    ( ~ ssList(nil)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f482]) ).

fof(f485,plain,
    ( spl0_6
  <=> nil = nil ),
    introduced(split_symbol_definition) ).

fof(f488,plain,
    ( ~ ssList(nil)
    | nil = nil
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[f298,f295]) ).

fof(f489,plain,
    ( ~ spl0_5
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f488,f482,f485]) ).

fof(f492,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f484,f223]) ).

fof(f493,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f492]) ).

fof(f494,plain,
    ( pd0_0(sk0_48,sk0_49)
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f423,f440]) ).

fof(f495,plain,
    ( pd0_0(sk0_48,sk0_47)
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f424,f494]) ).

fof(f496,plain,
    ( nil = sk0_47
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f495,f431]) ).

fof(f497,plain,
    ( nil = sk0_48
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f495,f430]) ).

fof(f498,plain,
    ( $false
    | spl0_0
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f497,f434]) ).

fof(f499,plain,
    ( spl0_0
    | ~ spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f498]) ).

fof(f500,plain,
    ( neq(sk0_47,nil)
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f424,f443]) ).

fof(f501,plain,
    ( frontsegP(sk0_48,sk0_49)
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f423,f447]) ).

fof(f502,plain,
    ( frontsegP(sk0_48,sk0_47)
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f424,f501]) ).

fof(f505,plain,
    ( spl0_7
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f507,plain,
    ( ~ ssList(sk0_47)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f505]) ).

fof(f508,plain,
    ( spl0_8
  <=> neq(sk0_47,nil) ),
    introduced(split_symbol_definition) ).

fof(f510,plain,
    ( ~ neq(sk0_47,nil)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f508]) ).

fof(f511,plain,
    ( spl0_9
  <=> frontsegP(sk0_47,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f513,plain,
    ( ~ frontsegP(sk0_47,sk0_47)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f511]) ).

fof(f514,plain,
    ( ~ ssList(sk0_47)
    | ~ neq(sk0_47,nil)
    | ~ frontsegP(sk0_47,sk0_47)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f425,f502]) ).

fof(f515,plain,
    ( ~ spl0_7
    | ~ spl0_8
    | ~ spl0_9
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f514,f505,f508,f511,f446]) ).

fof(f516,plain,
    ( spl0_10
  <=> neq(nil,nil) ),
    introduced(split_symbol_definition) ).

fof(f522,plain,
    ( spl0_12
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f524,plain,
    ( ~ ssList(sk0_48)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f522]) ).

fof(f535,plain,
    ( spl0_15
  <=> frontsegP(sk0_48,nil) ),
    introduced(split_symbol_definition) ).

fof(f537,plain,
    ( ~ frontsegP(sk0_48,nil)
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f535]) ).

fof(f538,plain,
    ( ~ ssList(nil)
    | ~ neq(nil,nil)
    | ~ frontsegP(sk0_48,nil)
    | ~ ssList(sk0_47) ),
    inference(resolution,[status(thm)],[f425,f295]) ).

fof(f539,plain,
    ( ~ spl0_5
    | ~ spl0_10
    | ~ spl0_15
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f538,f482,f516,f535,f505]) ).

fof(f545,plain,
    ( $false
    | spl0_1
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f496,f437]) ).

fof(f546,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f545]) ).

fof(f554,plain,
    ( ~ ssList(sk0_48)
    | spl0_15 ),
    inference(resolution,[status(thm)],[f537,f295]) ).

fof(f555,plain,
    ( $false
    | spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f554,f420]) ).

fof(f556,plain,
    spl0_15,
    inference(contradiction_clause,[status(thm)],[f555]) ).

fof(f567,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f524,f420]) ).

fof(f568,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f567]) ).

fof(f584,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f419,f507]) ).

fof(f585,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f584]) ).

fof(f586,plain,
    ( ~ ssList(sk0_47)
    | spl0_9 ),
    inference(resolution,[status(thm)],[f513,f286]) ).

fof(f587,plain,
    ( ~ spl0_7
    | spl0_9 ),
    inference(split_clause,[status(thm)],[f586,f505,f511]) ).

fof(f588,plain,
    ( $false
    | ~ spl0_3
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f510,f500]) ).

fof(f589,plain,
    ( ~ spl0_3
    | spl0_8 ),
    inference(contradiction_clause,[status(thm)],[f588]) ).

fof(f590,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f438,f445,f449,f489,f493,f499,f515,f539,f546,f556,f568,f585,f587,f589]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWC020+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 11:40:22 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.57  % Elapsed time: 0.020332 seconds
% 0.23/0.57  % CPU time: 0.049964 seconds
% 0.23/0.57  % Memory used: 16.179 MB
%------------------------------------------------------------------------------